Answer:
Option A
Step-by-step explanation:
We need to find two expressions that, when simplified, give the same results.
1) First, simplify the expression stated in the question. Multiply each of the terms in the parentheses by the number that is next to them. This would mean you have to multiply both 9x and -6 by 
. You also have to multiply 
and 
by 4. Then, simplify.
2) Now, combine the like terms.
So, we need to find which of the expressions listed equal 8x - 6.
3) Let's try option A. Do the same as before. Multiply each of the terms in the parentheses by the number that is next to them. So, multiply 4x and -12 by 
. Also, multiply 30x and 18 by 
. Then, combine like terms and simplify.
This also equals 8x - 6. Therefore, option A is the answer.
We assume the composite figure is a cone of radius 10 inches and slant height 15 inches set atop a hemisphere of radius 10 inches.
The formula for the volume of a cone makes use of the height of the apex above the base, so we need to use the Pythagorean theorem to find that.
h = √((15 in)² - (10 in)²) = √115 in
The volume of the conical part of the figure is then
V = (1/3)Bh = (1/3)(π×(10 in)²×(√115 in) = (100π√115)/3 in³ ≈ 1122.994 in³
The volume of the hemispherical part of the figure is given by
V = (2/3)π×r³ = (2/3)π×(10 in)³ = 2000π/3 in³ ≈ 2094.395 in³
Then the total volume of the figure is
V = (volume of conical part) + (volume of hemispherical part)
V = (100π√115)/3 in³ + 2000π/3 in³
V = (100π/3)(20 + √115) in³
V ≈ 3217.39 in³
Answer: x=15
Step-by-step explanation:
Equation: 107=(9x-115)+(4x+27)
Step 1: 9x+4x-115+27=107
Step 2: 13x-115+27=107
Step 3: 13x-88=107
Step 4: 13x-88+88=107+88
Step 5: 13x=195
Step 6: 13x/13=195/13
x=15
